[7stud]

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A very common situation that I run into (sorry, Crypto 1/2, ante 25c) is that I have a big split pair, like (xA)A, and complete the bring in on 3rd. One person calls. 4th street, we both catch blanks, I bet, they call. 5th street, we both catch blanks, I bet, they raise. At this point there is usually about $12 after their raise. It costs me 2 to call and 6 to see a showdown where the pot'll be 18ish.

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So the pot is offering you ($12 + $4) to $6 = 2.7 : 1 odds.

1) If your opponent has 2 pair, you are roughly a 1.4 : 1 underdog.
2) If your opponent has trips, you are a 9:1 underdog.

When an opponent raises with blanks to your "declared" Aces, you have to worry about trips. But, then you would have to wonder: why would trips raise and potentially lose their only customer. On 3rd street, you might have raised with a small pair and an Ace kicker, and a raise on 5th street could convince you to give up the hand and fold. If I had trips, I'd let you lead the betting the whole way and just call. So, trips seems like an unlikely holding.

If there is an 83% chance he has two pair and a 17% chance he has trips, then the odds are 2.7:1 against you winning the hand, which is the same as the pot odds you are getting. What do you estimate his odds of having trips are in that situation? If you think they are lower, then you can call.

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I've been folding this on boards where I see a 3-flush or a 3-straight, and I'm not very upset about this, though I'm not certain that it's right.

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1) If your opponent has a 4 flush with no dead cards, he is a slight favorite. With a couple of dead cards, you become the favorite.
2) If your opponent has a 4 flush with a pair and two dead flush cards, you are a slight favorite.
3) If your opponent has 2 pair, you are roughly a 1.4: 1 underdog
4) If your opponent has a made flush, you are roughly a 9:1 underdog.
5) If your opponent has trips, you are roughly a 9:1 underdog.

First, a good player is not going to play a flush draw against a single opponent without overcards, and since you have an Ace up(?), a made flush is not very likely. Playing a flush draw against a lone opponent does not offer you a high enough pay off when you hit the flush to compensate you for all the money you put in the pot when you play and miss.

Once again, you have to question why someone with trips or a made flush on 5th street would raise you and risk losing their only customer. You might want to try checking there, and letting them lead the betting. Of course the risk is, they may check behind you and end up getting a free card.